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Resilience
Resilience is a character attribute that reduces the chance to receive critical strikes or spell critical strikes, reduces the effect of mana drain spells, reduces the damage taken from critical strikes and spell critical strikes, and reduces the damage taken from damage over time effects. Characters have no innate resilience. It can only be gained through external sources, e.g. equipment, elixirs, enchantments, gems, and some spell effects that grant resilience rating. Many items and recipes that grant resilience rating are PvP rewards. Resilience was introduced with the Burning Crusade expansion as part of the new combat rating system. Previously, no such resilience mechanic existed — as a result, resilience rating only appears on items available to players over level 60, with some rare exceptions. Formulas One percent of resilience has the following effects: * Chance to be critically hit reduced by 1%. * Damage taken from crits that do land have their critical strike damage component reduced by 2.2%. * Damage taken from DoTs reduced by 1%. * Amount of mana drained or burned by mana draining effects is reduced by 2.2%. (added in Patch 2.4) As part of the combat rating system, the amount of resilience rating needed to get a certain amount of resilience increases with level. A higher level player will need more resilience rating to get the same effect as a lower level player. At level 70, a player needs 39.4 resilience rating to get 1% of resilience. Remember that resilience only affects the components of an attack directly related to a critical strike and DoTs. It does absolutely nothing that affects a normal hit component of any attack. Damage mitigation The effect of resilience is related to the equations for calculating critical strike damage. A player's average damage caused for a single spell or ability is given by the following equation, where C'' is the critical strike rate, and ''B is the critical strike damage bonus component. That is, how much extra damage a critical strike gives compared to a normal hit. Percentages are expressed in decimal form (i.e. a number between 0 and 1). Melee attacks typically have a value B'' of 1.0 (100%), spells a value ''B of 0.50 (50%). However most classes have talents that can increase the bonus B'' for certain spells or abilities. Avg. Damage = Damage * (1.0 - C) + Damage * (1.0 + B) * C The first half of the equation is damage dealt from hits and the second part is damage dealt from crits, with each weighted by the probability of it occurring. For the purposes of analyzing resilience, we only consider attacks that deal damage, which will be hits and crits in PvP combat. Note that (1.0 - C) in the first half and C in the second half add up to 100%. For example, a warlock using Shadow Bolt who has the Ruin talent will have a critical strike bonus ''B of 1.0 (100%) for that spell. This particular warlock also has a crit rate of 0.30 (30%) with Shadow Bolts. If a non-crit is 2000, and a crit is 4000, then the average over all Shadow Bolts will be 2600. Avg. Damage = * (1.0 - 0.30) + * (1.0 + 1.0) * (0.30) Avg. Damage = * 0.70 + * 2.0 * 0.30 = 2600 Resilience modifies the C'' variable and the crit damage portion of the equation. The critical strike rate is directly reduced, and the crit damage is multiplied by a reduction factor. The updated equation for average critical strike damage where ''res is the target's resilience as a percentage reduction is given below: Avg. Damage = Damage * (1.0 - (C - res)) + Damage * (1.0 + B) * (C - res) * (1.0- 2*res) For the warlock example above, if the target has 1% resilience the base damage is unaffected, Shadow Bolt hitting for 2000, but it will crit only 29% of the time, and will only do 3920 damage. The average damage per Shadow Bolt however will now be 2556.80. Compared to a 2600 average with no resilience, the target with 1% resilience will receive 2% less damage (4000*0.98) per critical strike and 1.692% less damage overall from this warlock's Shadow Bolts. Avg. Damage = * (1.0 - (0.30 - 0.01) + * 2.0 * (0.30 - 0.01) * (1.0 - 2*0.01) Avg. Damage = * 0.71 + * 2.0 * 0.29 * 0.98 = 2556.80 As an extreme example, consider a rogue who has a 100% crit rate with a standard weapon attack. Melee attacks have a critical strike bonus of 100%. If the average attack is 200, crits are 400. With a 100% crit rate every attack should now crit for 400. If the target has 1% resilience then only 99% of attacks will critically strike and the damage of those crits will be reduced by 2%. One out of every hundred attacks will now only hit for 200, and the rest will still be critical strikes but only deal 392 damage. This means the average attack is now reduced to 390.08 overall resulting in 2.480% total damage reduction. Avg. Damage = * (1.0 - (1.0 - 0.01) + * 2.0 * (1.0 - 0.01) * (1.0 - 2*0.01) Avg. Damage = * 0.01 + * 2.0 * 0.99 * 0.98 = 390.08 Now, consider the same rogue attacking targets with 2% and 3% resilience. Avg. Damage = * (1.0 - (1.0 - 0.02) + * 2.0 * (1.0 - 0.02) * (1.0 - 2*0.02) Avg. Damage = * 0.02 + * 2.0 * 0.98 * 0.96 = 380.32 Avg. Damage = * (1.0 - (1.0 - 0.03) + * 2.0 * (1.0 - 0.03) * (1.0 - 2*0.03) Avg. Damage = * 0.03 + * 2.0 * 0.97 * 0.94 = 370.72 2% resilience reduces incoming damage by 4.92% (a 2.44% increase over 1%) and 3% resilience reduces incoming damage by 7.32% (a 2.40% increase over 2%). There's an insignificant diminishing returns effect on overall damage reduction for each additional amount of resilience. It should be obvious that the smaller the critical strike components are in any attack the less of an effect a targets resilience will have. Consider a mage casting a 1000 damage untalented Frostbolt with a 20% chance to critically strike and a damage bonus of 50%. Against a target with no resilience, the average damage per Frostbolt is 1100. Avg. Damage = * (1.0 - 0.20) + * (1.0 + 0.5) * (0.20) Avg. Damage = * 0.80 + * 1.5 * 0.20 = 1100 Now against a target with 3% resilience. Avg. Damage = * (1.0 - (0.20 - 0.03) + * 1.5 * (0.20 - 0.03) * (1.0 - 2*0.03) Avg. Damage = * 0.83 + * 1.5 * 0.17 * 0.94 = 1069.7 The 3% resilience is only reducing overall damage from Frostbolt by 2.754%, where it was reducing damage from the crit-happy rogue by 7.32%. Now consider the same Frostbolt, talented with Ice Shards. (crit. component doubled) Avg. Damage = * (1.0 - 0.20) + * (1.0 + 1.0) * (0.20) Avg. Damage = * 0.80 + * 2.0 * 0.20 = 1200 Now against a target with 3% resilience. Avg. Damage = * (1.0 - (0.20 - 0.03) + * 2.0 * (0.20 - 0.03) * (1.0 - 2*0.03) Avg. Damage = * 0.83 + * 2.0 * 0.17 * 0.94 = 1149.6 The overall damage reduction is now 4.2%. Resilience rating required per 1% Levels 60 through 70 use the following formula: Rating for 1% resilience = 2050/(262-(3* Level)) Levels 8 through 60 use the following formula: Rating for 1% resilience = (Level - 60) * (0.48) + 25 These two formulas result in the chart below: For any given level, divide your rating by the factor in the chart. For example, total resilience rating on items is 20 at level 39 it would equal 1.34 % resilience. 20 / 14.92 = 1.34 % resilience. It's a straight multiplication if you wanted to know what rating you needed at any given level for any amount of resilience. There are no diminishing returns on resilience. Doubling the rating doubles the effect for any given level. Tripling the rating triples the %, etc. For example, if you wanted to know what rating you needed at level 52 for 4.7% resilience, multiply (21.14 * 4.7) = 99.45 rating. 0.45 not rating is possible because rating is in whole numbers. You always have to round up. For a minimum of 4.7% resilience at Level 52 you would need a 100 rating. Resilience cap The damage reduction from a critical strike is capped at 33%, which equates to 1353 resilience at level 80. However, there is currently no cap on DoT reduction or critical strike chance reduction. Enhancements Arcanum of the Savage Gladiator: Permanently adds 30 stamina and 25 resilience rating to a head slot item. Arcanum of the Gladiator: Permanently adds 18 Stamina and 20 resilience rating to a head slot item. Arcanum of Dominance: Permanently adds 29 spell power and 20 resilience rating to a head slot item. Arcanum of Triumph: Permanently adds 50 attack power and 20 resilience rating to a head slot item. Inscription of Dominance: Permanently adds 23 spell power and 15 resilience rating to a shoulder slot item. Inscription of Triumph: Permanently adds 40 attack power and 15 resilience rating to a shoulder slot item. Earthen Leg Armor : Permanently adds 28 stamina and 40 resilience rating to a leg slot item (added at patch 3.0.8). Elixirs Elixir of Ironskin: Increases Resilience Rating by 30 for 60 min. Flasks Lesser Flask of Toughness: Increases Resilience Rating by 50 for 60 min. Enchantments Enchant Chest - Major Resilience: Permanently enchant a piece of chest armor to grant 15 resilience rating. Enchant Chest - Exceptional Resilience: Permanently enchant chest armor to increase resilience rating by 20. Enchant Shield - Resilience: Permanently enchant a shield to grant 12 resilience rating. Gems Patch 2.4 Resilience now reduces the effects of mana-drain spells by the same amounts it reduces critical strike damage (capped at 25%, 492.8 resilience required for this number) Patch 3.0.3 From the patch notes: Resilience: The damage reduction component of resilience has been increased from 2 times the critical strike chance reduction to 2.2 times the critical strike chance reduction. In addition, the maximum damage reduction to a critical strike from resilience has been increased from 30% to 33% (1353 resilience at level 80). See also *Combat rating system *Critical strike *Spell critical strike Category:Game terms Category:Combat Category:Attributes Category:Formulas and game mechanics